A significant shortcoming of concealed head self-clinching studs and standoffs is that a hole must first be counterbored using a flat end mill wherever a fastener is intended to be installed. Past efforts to design self-piercing or self-attaching fasteners which do not require a hole in the substrate material include nails and rivets which can be driven into soft substrate material relative to the hardness of the fastener. In many cases, a special anvil is required to support the back side of the sheet which cooperates with the configuration of the driven, piercing end of the fastener so that the penetrating end deforms to clinch into the sheet. The penetrating end of the fastener may be heat treated to a hardness which is greater than the hardness of the structural metallic member into which the fastener is driven. Despite the past efforts in this field, there still exists a need for an economical and effective self-attaching fastener which does not require a mounting hole or a specially configured supporting anvil to achieve secure attachment of the fastener to the supporting substrate.